KU Leuven vibro-acoustics activities in an Industry 4.0 ... · KU Leuven vibro-acoustics activities in an Industry 4.0 context Wim Desmet KU Leuven – Department of Mechanical Engineering

KU Leuven vibro-acoustics activities in an Industry 4.0 context

Wim Desmet

KU Leuven – Department of Mechanical EngineeringFlanders Make - Virtual Department Mechatronics & Design

overview

• KU Leuven team

• Industry 4.0 - research strategy and approach

• some vibro-acoustic innovations:

o virtual sensing

o “metamaterials by design”

o model based geometry characterisation

o model based material characterisation

www.kuleuven.be

KU Leuven

• founded in 1425

• 70000 students

• 15 faculties, 50 departments

• 62 academic programmes

• 800 MEUR total revenues

who we are

team

• KU Leuven

o Department of Mechanical Engineering• Division of Production engineering, Machine design and Automation (PMA)

• Noise and Vibration Research Group (MOD)

• research staffo 5 academic and 1 associated

o 1 industrial research manager

o 11 postdoctoral researchers

o 61 PhD incl. 10 industrial PhD res.

• areas of research application domainso vibro-acoustics

o aero-acoustics

o multi-body dynamics

o smart system dynamics

o structural reliability & uncertainty

• core lab of the Strategic Research Centre for Smart Manufacturing

(Flanders Make)

- energy and environment

- transport and mobility

- health

- advanced manufacturing

Industry 4.0

enablers

full digitization of the value chain

smart connected customized

cyber-physical systems

Model Based System Engineering

digital twin

Industry 4.0

strategy

creating added value

by embedding dynamic behavior information

in a digital twin

during every phase (design – manufacturing – operations)

approach

physical behaviour models

• vibro-acoustics• (flexible) multibody dynamics • multi-physical mechatronic system models• aero-acoustics

research innovations

• methodological • MBSE applications

model usage

• purely virtual (virtual prototyping)• blended with sensors (virtual sensing)

overview

• KU Leuven team



o virtual sensing




some vibro-acoustic innovationsmodel based virtual sensing

objectives

• obtain information on hard-to-measure quantities from high-

fidelity first-principles dynamic models, of which the inputs and

parameters are estimated on-line and in-situ using

affordable/non-intrusive sensor data

• to be used in all phase (design – manufacturing – operational

life) of a cyber-physical system

virtual sensingmodels time-stable

estimators

non-intrusive

sensors

HW/SWarchitecture

Naets, F., Croes, J., Desmet, W. (2015). An online coupled state/input/parameter estimation approach for structural dynamics. Computer Methods in Applied Mechanics and Engineering. 283 (1) 1260-1277

Kalman Filter

EKF/UKF

Moving Horizon Estimators


approach

Estimator

Input

hpredicted

xestimated

hestimated

Model

xestimated

Measurements

Kalman filter

hmeasured


approach


approach


objectives

• obtain information on hard-to-measure quantities from high-

fidelity first-principles dynamic models, of which the inputs and

parameters are estimated on-line and in-situ using

affordable/non-intrusive sensor data

challenges

• efficient, time stable physical behaviour models

• observability

approach

• stable observers

• high-fidelity physical behaviour models

• non-intrusive sensors


time-stable coupled vibro-acoustic model order reduction

vibro-acoustic finite element modelvibro-acoustic finite element model

Time-Domain simulation

Time-Domain simulation

Reduced-Order Model

Reduced-Order Model

Xtoo expensive Xstandard MOR:

becomes unstable!Stability-preserving MOR

van de Walle, A., Naets, F., Deckers, E., Desmet, W. (2017). Stability-preserving model order reduction for time-domain simulation of vibro-acoustic FE models. International Journal for Numerical Methods in Engineering. (in press)



�� t + �� t + � t = �(t)

�� t + �� t + �� t = ��(t)

n equations in n unknowns

r equations in r unknowns



• coupled vibroacoustic FE system of equations:

is stable!

• MOR:

with reduced matrices

• after projection of K, C and M matrices: partial symmetry and definiteness is destroyed, resulting in a loss of stability



• one-sided projection

• transform into linear descriptor formulation

• stiffness matrices : symmetric positive (semi)definite

• mass matrices : symmetric positive definite

• damping matrices : positive (semi)definite

finite element model reduced-order model

number of DOFs 564 228 260

model reduction time n/a 2,7h

FRF computation time 76,4h 3,6s




validation: (real-time) vibro-acoustic digital twin



Virtual sensing at microphone R2

close-up



Virtual sensing at microphone R2





virtual measurement of plate stiffness

� = �� 0 ��

estimate scaling factor � on structural stiffness matrix => identify

plate E-modulus

� = �� 0 ��

coupling matrix

acoustic stiffness matrix

structural stiffness matrix


validation: microphone based parameter estimation

identified value

initial guess

Computational time ≅ 2 minutes

different start values converge to the same estimate





overview

• KU Leuven team



o virtual sensing




some vibro-acoustic innovations“metamaterials by design”

objectives

material systems with good noise and vibration insulation properties

at

o low-mass

o low-volume

o low-frequency

o low-manufacturing cost

approach

• resonant meta-materials

• stopband behaviour at selected design frequencies

+20% mass

(local)

+20% mass

(spread)Target

Frequency [Hz]

AverageDisplacement

[dB]

Propagation Direction

unit cell modelling

Stop Band


Resonant Inclusions


12.5 mm12.5 mm

mass

spring


http://youtu.be/hMCfRHshjXc


unit cell modelling

Finite structure

modelling

Propagation direction

?

what about• attenuation factors• topology optimisation• sound transmission loss

predictions


• from classical inverse approach

• to direct solution approach based

on Wave FEM Approach, allowing

o imaginary and real wavenumbers

o and inclusion of damping in materials

L. Van Belle, C. Claeys, E. Deckers, W. Desmet, Modelling, analysis and experimental validation of locally resonant metamaterials including damping, Journal of Sound and Vibration, under review


unit cell modelling - damping

• density-based topology optimization: single phase layouts

(solid-void) are considered.

o starting from solid plate

o enforcing resonant behaviour

L. Noël, C. Claeys, E. Deckers, W. Desmet, WCSMO 12 (5-9 June 2017, Braunschweig, Germany): Designing metamaterials for enhanced noise and vibration properties.


unit cell modelling – topology optimization

• hybrid method

o wave based method: acoustic domains

o FEM: structural domain

• predicts absorption and transmission for 2D infinite periodic structures

FEM

WBM

WBM

E. Deckers, S. Jonckheere, L. Van Belle, C. Claeys, W. Desmet, Prediction of transmission, reflection and absorption coefficients of periodic structures using a hybrid Wave Based - Finite Element unit cell method Journal of Comp.Physics, under review


unit cell modelling – sound transmission loss

70 mm70 mm

overview

• KU Leuven team



o virtual sensing




some vibro-acoustic innovationsmodel based geometrical characterisation

objectives

• dimensional quality control of manufactured structures

through vibro-acoustic testing

approach

• vibro-acoustic models with a direct link to the geometrical

parameters

• vibro-acoustic testing (dynamic input – accelero/mic responses)

• inverse method: retrieve geometrical parameters from dynamic

response measurements

challenge

• isogeometrical analysis models – linking digital geometry with

functional (vibro-acoustic) performance


IGA – IsoGeometrical Analysis for vibro-acoustics

design throughanalysis

CAE bottleneck = pre-processing: CAD geometry ≠ CAE geometry

isogeometric: use CAD descriptions directly in CAE

⤷ NURBS for both geometry & field variable

⟹⟹⟹⟹ no meshing

⟹⟹⟹⟹ smoother shape functions

⤷ less numerical dispersion

quadratic splines quadratic polynomials



• lack of volumetric discretizations: CAD = object envelope= surface

• complex representations of free-form geometriesNURBS = tensor product ≠ free-form

⤷ free-form CAD = multipatch NURBS

= trimmed



IGA for vibro-acoustics: main challenges

• Lack of volumetric discretizations: CAD = object envelope= surface

• Complex representations of free-form geometriesNURBS = tensor product ≠ free-form

⤷ free-form CAD = multipatch NURBS

= trimmed

⟹ isogeometric BEM

⟹ multipatch coupling techniques

L. Coox, O. Atak, D. Vandepitte, W. Desmet. An isogeometric indirect boundary element method for solving acoustic

problems in open-boundary domains, Comput. Methods Appl. Mech. Engrg., 316:186-208, 2017.

L. Coox, F. Greco, O. Atak, D. Vandepitte, W. Desmet. A robust patch coupling method for NURBS-based isogeometric

analysis of non-conforming multipatch surfaces, Comput. Methods Appl. Mech. Engrg., 316:235-260, 2017.

Isogeometric BEM: bass-reflex loudspeaker

49

37 NURBS patches72 interfaces


50


51

2000 Hz

Directivity plot [dB]

1m radius

1000 Hz500 Hz

• to be exploited for geometrical characterization

• to be exploited for dimensional quality control.


• starting from a reference CAD model of the component, the

geometry is updated using the information from the

measurements.

• following the framework of IGA shape optimization, the

control points can be directly used as optimization variables.


• an optimization problem is solved and the exact geometry can be extracted from the updated IGA model.

• since a high accuracy is required, many control points are used for the optimization and MOR is applied.


overview

• KU Leuven team



o virtual sensing




some vibro-acoustic innovationsmodel based material characterisation

objectives

• retrieving material parameters through vibro-acoustic testing

approach

• vibro-acoustic model including parameterized material models

• vibro-acoustic testing (dynamic input – accelero/mic responses)

• inverse method: retrieve material parameters from dynamic

response measurements

challenge

• efficient vibro-acoustic models for a family of material parameter

values .... parametric Model Order Reduction (pMOR)

parametric Model Order Reduction (pMOR)

o accurate model for large parameter range

o high on-line performance • small reduced order model

• stable

o off-line calculation time is not that important

� goal:

where


two main approaches:

1) global basis � and �concatenate the local bases

2) interpolation of local information

local bases or local reduced order matricesp1

p2

p3 ••

••

parametric Model Order Reduction (pMOR)


pMOR application – model updatingby parameter optimization

Full order modelDOF : 22904Computational time : 5h

parametric reduced order modelDOF : 180Computational time : 2s


Initial design parameters Optimized design parameters

�� 0 �� + �� !� + "�� 0

0 �!� + "�� # �$ !� 0#�%& !�

'( = )�

)�

argmin01,34516(78),34516(98),34516(7:),34516(9:)

log�= > ()?)@A0 # )?)BCD)$BEFGH

IJ�


Matrix-free MOR scheme - Basics

= Reduced Order Modelling scheme to further speed-up FRF calculations

• Iterative Adaptively enriched

• Rational Rational interpolation functions

• Krylov Based on system responses (non-modal)

• Matrix-free No explicit system matrices necessary

= BLACK BOX

, �,� , �,�

Matrix-free MOR scheme – Procedure

1. Get the system transfer functions for the input-output pairs you are interested in, e.g. from LTI formulation:

2. Apply matrix-free formulation of rational Krylov projection to build theROM matrices [∎M]OP using left (i) and right (j) projection vectors

3. Calculate the approximated full system response from the ROM at allfrequencies

4. (Iterative enrichment until convergence)

[Q RS]OP =ωR$HOP ωR #ωS$HOP ωS

ωR$ # ωS$[�Q RS]OP =

HOP ωR # HOP ωSωR$ # ωS$

[VQ R]OP = HOP ωR [WX SY]OP = HOP ωS

HQOP � = HOP ωS #ω$�QOP + QOPZ�HOP ωR

Matrix-free MOR scheme – Application

Plate (0.5x0.25x0.0006m)• Steel

• Boundary condtions

o Symmetry edges (red)

o Clamped edges (green)

• Boundary acceleration

• Center point response

Treatment (0.49x0.34x0.0015m)

• CLD

o 1.373mm soft rubber

o 127µm aluminium sheet)

100 102 104 106103

106

109

Frequency [Hz]

100

102

104

106

0

2

4

Matrix-free MOR scheme – Results

Bare Constr.

# Full DOF 6482 38601

# Iterations 27 11

# Frequencies (red.)

54 22

# Frequencies(full)

999 999

Speed-up 18.5x 45.5x

thank you

Wim Desmet

Celestijnenlaan 300B – box 24203001 Leuven, Belgiumtel +32 16 32 25 57mobile +32 479 531578

[email protected]

www.mech.kuleuven.be/mod

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KU Leuven vibro-acoustics activities in an Industry 4.0 ... · KU Leuven vibro-acoustics activities in an Industry 4.0 context Wim Desmet KU Leuven – Department of Mechanical Engineering